Remark 3.11 If \(X\)  and \(Y\)  are special varieties over \(k\) , then \(X\times Y\)  is special [1]}. Thus, the product theorem for the weak-Hilbert property is in accordance with the conjecture of Campana and Corvaja-Zannier (Conjecture REF ) that a variety is special if and only if it has the weak-Hilbert property over some finite field extension of the base.

